Existence and destruction of tori in a discontinuous oscillator under quasi-periodic excitations

Pengcheng Miao; Jicheng Duan; Denghui  Li; Jianhua  Xie; Celso Grebogi

doi:10.1016/j.physd.2025.134804

Existence and destruction of tori in a discontinuous oscillator under quasi-periodic excitations

Pengcheng Miao
, Jicheng Duan
, Denghui Li^* (Corresponding Author)
, Jianhua Xie
, Celso Grebogi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

We investigate the existence and destruction of invariant tori in a discontinuous oscillator under quasi-periodic excitation. For the conservative case, by constructing a quasi-periodic twist map, we prove the existence of infinitely many invariant tori and show that all solutions of the system are bounded when the frequencies satisfy the non-resonance condition. For the dissipative case, by taking a quasi-periodic forcing with two frequencies, we employ numerical methods to explore the breakdown mechanisms of torus attractors and multistability phenomena. The multistability includes the coexistence of multiple torus attractors and the coexistence of torus and chaotic attractors. In addition, we show that grazing bifurcations induce the destruction of torus attractors with the emergence of either chaotic attractors or strange nonchaotic attractors.

Original language	English
Article number	134804
Number of pages	11
Journal	Physica. D, Nonlinear Phenomena
Volume	481
Early online date	1 Jul 2025
DOIs	https://doi.org/10.1016/j.physd.2025.134804
Publication status	Published - Nov 2025

Bibliographical note

The authors are very grateful to the reviewers for their careful investigations and valuable suggestions during the revision of the paper.

Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Funding

This work is supported by the National Natural Science Foundation of China (12362002, 12202168, 12172306).

Funders	Funder number
National Natural Science Foundation of China	12362002, 12202168, 12172306

Keywords

discontinuous oscillator
quasi-periodic excitation
invariant tori
strange nonchaotic attractor

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Cite this

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abstract = "We investigate the existence and destruction of invariant tori in a discontinuous oscillator under quasi-periodic excitation. For the conservative case, by constructing a quasi-periodic twist map, we prove the existence of infinitely many invariant tori and show that all solutions of the system are bounded when the frequencies satisfy the non-resonance condition. For the dissipative case, by taking a quasi-periodic forcing with two frequencies, we employ numerical methods to explore the breakdown mechanisms of torus attractors and multistability phenomena. The multistability includes the coexistence of multiple torus attractors and the coexistence of torus and chaotic attractors. In addition, we show that grazing bifurcations induce the destruction of torus attractors with the emergence of either chaotic attractors or strange nonchaotic attractors.",

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T1 - Existence and destruction of tori in a discontinuous oscillator under quasi-periodic excitations

AU - Miao, Pengcheng

AU - Duan, Jicheng

AU - Li, Denghui

AU - Xie, Jianhua

AU - Grebogi, Celso

N1 - The authors are very grateful to the reviewers for their careful investigations and valuable suggestions during the revision of the paper.

PY - 2025/11

Y1 - 2025/11

N2 - We investigate the existence and destruction of invariant tori in a discontinuous oscillator under quasi-periodic excitation. For the conservative case, by constructing a quasi-periodic twist map, we prove the existence of infinitely many invariant tori and show that all solutions of the system are bounded when the frequencies satisfy the non-resonance condition. For the dissipative case, by taking a quasi-periodic forcing with two frequencies, we employ numerical methods to explore the breakdown mechanisms of torus attractors and multistability phenomena. The multistability includes the coexistence of multiple torus attractors and the coexistence of torus and chaotic attractors. In addition, we show that grazing bifurcations induce the destruction of torus attractors with the emergence of either chaotic attractors or strange nonchaotic attractors.

AB - We investigate the existence and destruction of invariant tori in a discontinuous oscillator under quasi-periodic excitation. For the conservative case, by constructing a quasi-periodic twist map, we prove the existence of infinitely many invariant tori and show that all solutions of the system are bounded when the frequencies satisfy the non-resonance condition. For the dissipative case, by taking a quasi-periodic forcing with two frequencies, we employ numerical methods to explore the breakdown mechanisms of torus attractors and multistability phenomena. The multistability includes the coexistence of multiple torus attractors and the coexistence of torus and chaotic attractors. In addition, we show that grazing bifurcations induce the destruction of torus attractors with the emergence of either chaotic attractors or strange nonchaotic attractors.

KW - discontinuous oscillator

KW - quasi-periodic excitation

KW - invariant tori

KW - strange nonchaotic attractor

U2 - 10.1016/j.physd.2025.134804

DO - 10.1016/j.physd.2025.134804

M3 - Article

SN - 0167-2789

VL - 481

JO - Physica. D, Nonlinear Phenomena

JF - Physica. D, Nonlinear Phenomena

M1 - 134804

ER -

Existence and destruction of tori in a discontinuous oscillator under quasi-periodic excitations

Abstract

Bibliographical note

Data Availability Statement

Funding

Keywords

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